Integral de $$$81 x^{20}$$$

Halla $$$\int 81 x^{20}\, dx$$$.

Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=81$$$ y $$$f{\left(x \right)} = x^{20}$$$:

$${\color{red}{\int{81 x^{20} d x}}} = {\color{red}{\left(81 \int{x^{20} d x}\right)}}$$

Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=20$$$:

$$81 {\color{red}{\int{x^{20} d x}}}=81 {\color{red}{\frac{x^{1 + 20}}{1 + 20}}}=81 {\color{red}{\left(\frac{x^{21}}{21}\right)}}$$

Por lo tanto,

$$\int{81 x^{20} d x} = \frac{27 x^{21}}{7}$$

Añade la constante de integración:

$$\int{81 x^{20} d x} = \frac{27 x^{21}}{7}+C$$

$$$\int 81 x^{20}\, dx = \frac{27 x^{21}}{7} + C$$$A